To analyze the arithmetic sequence given by the formula \( a_n = 3.7 + \frac{1}{2} n \), we first need to determine the general term and then calculate the 9th term.
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The general formula for the nth term of the arithmetic sequence is given by: \[ a_n = a + (n-1)d \] Here, \( a \) is the first term, and \( d \) is the common difference.
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From the formula \( a_n = 3.7 + \frac{1}{2} n \), we can identify:
- The first term, when \( n = 1 \): \[ a_1 = 3.7 + \frac{1}{2} \cdot 1 = 3.7 + 0.5 = 4.2 \]
- The common difference \( d \) is \( \frac{1}{2} \).
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To find the 9th term (\( a_9 \)): \[ a_9 = 3.7 + \frac{1}{2} \cdot 9 = 3.7 + 4.5 = 8.2 \]
Thus, the 9th term, rounded to the nearest tenth, is 8.2.
Among the options provided (10.6, 4.28, 8.2), the correct answer is 8.2.